... Computational dynamics Continuation Methods Bio-mechanical systems Biological systems The continuum mechanics-based elastic rod models [ 1 , 2 ] have evolved as viable tools to efficiently simulate the bending and twisting deformations of a variety of slender structures. Slender structures occur...

... , A. , and Hald , O. , 2009 , Stochastic Tools in Mathematics and Science , Vol. 1 , Springer, New York. [16] Gardiner , C. , 1985 , Stochastic Methods , Springer-Verlag, Berlin. [17] Allgower , E. L. , and Georg , K. , 2003 , Introduction to Numerical Continuation Methods , Society...

... hydrodynamic journal bearing is investigated near the stability threshold using two degrees-of-freedom model and compared with short hydrodynamic journal bearing. The stability of the system depends on the nondimensional bearing parameter, shaft rotational speed, and unbalance. Numerical continuation method...

..., especially if some displacements are prescribed. Once a static solution has been found, the linearized equations of motion about this solution can be obtained in terms of a set of minimal coordinates, that is, in the degrees-of-freedom (DOFs). In addition, a continuation method is described for tracing...

... with the lattice fractional diffusion equation in terms of Riesz Caputo difference. Continuation Methods Fractional calculus 17 05 2017 11 07 2017 Contributed by the Design Engineering Division of ASME for publication in the J OURNAL OF C OMPUTATIONAL AND N ONLINEAR D YNAMICS...

.... 22 09 2016 07 09 2017 Algorithms Continuation Methods Fractional calculus Numerical Integration methods In the past few decades, fractional calculus has been used in several areas of science and engineering; see Refs. [ 1 – 7 ]. However, not all systems are best described...

... domain via the harmonic balance method (HBM), and then, the equations of motion are solved by an arc-length continuation method. After comparisons with published data on beams with rectangular cross section and on carbon nanotubes (CNTs), the study focuses on the nonlinear modes of vibration of CNTs...

... of Forced Nonlinear Systems Using Shooting/Arc-Length Continuation Method-Application To Rotor Systems ,” ASME J. Vib. Acoust. , 119 ( 1 ), pp. 9 – 20 . 10.1115/1.2889694 [12] Sundararajan , P. , and Noah , S. T. , 1998 , “ An Algorithm for Response and Stability of Large Order Non-Linear...

.... [42] Allgower , E. E. L. , and Georg , K. , 2003 , Introduction to Numerical Continuation Methods (Classics in Applied Mathematics), Vol. 45 , Society for Industrial and Applied Mathematics , Philadelphia, PA. [43] Rao , A. V. , 2009 , “ Survey of Numerical Methods for Optimal...

... . Manuscript received November 20, 2015; final manuscript received May 6, 2016; published online May 24, 2016. Assoc. Editor: Dumitru Baleanu. 20 11 2015 06 05 2016 Algorithms Bifurcations Chaotic dynamics Continuation Methods Fractional calculus Integration methods Generally...